Quadratic Forms and Their Classification by Means of Invariant Factors, Vol. 3 (Classic Reprint) - Hardcover

T. J. I'A Bromwich

Hardcover

ISBN 10: 0266397093 ISBN 13: 9780266397090

Publisher: Forgotten Books, 2017

Synopsis

Explore how quadratic forms are classified with invariant-factors and Kronecker's invariants.

This rigorous, graduate‑level text explains reduction methods, theorems, and practical applications that connect algebra to geometry, with clear pathways from theory to conics and quadrics.

The book develops a step‑by‑step approach to reducing families of quadratic forms, discusses regular minors and Weierstrass’s and Sylvester’s contributions, and shows how invariant‑factors remain stable under transformations. It blends detailed proofs with worked examples to illustrate reduction in three and four variables, the role of determinant factors, and the geometric meaning behind the algebra.
What you’ll experience

• Foundations of invariant‑factors and their invariance under linear substitutions
• Techniques for reducing a family of quadratic forms to standard types
• Connections between algebraic factors and geometric objects like conics and quadrics
• Guided examples in multiple variables and discussions of singular cases

Ideal for readers of advanced algebra and geometry who want a structured, reference‑style treatment of quadratic forms and their classification.

Edition details

• Publisher: Forgotten Books
• Publication date: 2017
• Language: English
• ISBN 10: 0266397093
• ISBN 13: 9780266397090
• Binding: Hardcover
• Number of pages: 117